Frequency modulation system



Nov. 9, 1948. L E. NoRToN FREQUENCY MODULATION SYSTEM 5 Sheefs-Sheet 1 Filed Feb. 26, 1945 IN V EN TOR.

Nov. 9, 1948. V L. E.. NoRTN 2,4531453 FREQUENCY MODULATION SYSTEM med Feb. 26, 1945 s Sheen-sheet 2 faim/lt;

mal/Mraz AAAAAAAAAAAAAA R'Y' 'VV kw. N Q* v v I i i 'nun .k v N :L 1' I 4 i 4 g 1 '1 N b m Y n w .T a T L l Q! AAAAAAA l'! A l 4 H VVVWWWW e' IM w BY k I f w* r NOV. 9, 1948. .E NOR-[ON V 2,453,453

-* FREQUENCY MODULATION SYSTEM Y s/JA Nov. 9, 1,948. L. E. NoRTN 2,453,453

I I FREQUENCY MODULATION SYSTEM Filed Feb. 26, 1945 5 Sheets-Sheet 4 :esaw

. I N V EN TOR.

low/:EE Jlfor-In 11 I BY Nov. 9, '1948. E NORTON I 2,453,4s3

FRE QUENCY MODULATION SYSTEM med Feb. 26, 1945 4 s sugas-sheet:

INVENTOR.

LowaIlEJlflion C-QML l-.tmisa t; se' z,45t,' 4s3 memor monnm'rrou sr's'mu Lowell E. Norton, Princeton Junction, N. I., asi i linor to Radio Corporation of America, a cor-- poration of Delaware i Application February 28, 1945, Serial No. 579.787

v transmission systems. and

I This invention relates generally to signal more particularly to improved methodsl of and means for modulating the frequency of signal generating systems by which is then parallel-resonated' another 2 i reactance of opposite sign. 'I'he variable syn thetic control resonator thus provided is parallel-connected to the generator and load, and theiinpedance of the control resonator is varied in means of control resonator networks, the char- 5 response to signal intelligencetto modulate the acteristics of which are varied in response to frequency of the generator. 1 o signal intelligence. Circuit elements having rapid rates of change iSubstantlally linear frequency'modulation .of of phase angle with frequency and critical magnetrons or other ultra-high frequency genoptimum line lengths may be determined, as deerators has become of increasing importance due scribed Vin detail hereinafter, to provide practo the widespread use of such deviceslas sources tical circuit conflgurations. It is emphasized of ultra-high frequency energy. Stable and that the instant system diifers basically from linear frequency modulatlon is particularly necprevious practice wherein the wreactive elements essary whenthe magnetron or other high freof a high "Q" resonator are first combined, and quencysource must operate unattended for comlb then transformed to new values, the transparatively long intervals during which ambient formed resonator' impedance being shunt-contemperatures, terminal impedflncs. Operating nected with the generator and load. potentials and currents and magnetic field char- The present invention is an improvement over acteristics may fluctuate or vary between wide the system disclosed in my copending U. LS. aplimits. i plication, Serial No. 579.766, filed February 26,\ The methods of and means for frequency 1945, entitled Method of and means for fremodulating such devices, -to be described in dequency stabilizing frequency generators." astail hereinafter. may be emplovedv at any fresigned to the same assignee as the instant apquency. They areV particularly convenient when plication, v the frequency iS Sllficlently high so that the use The system is effective in reducing undesirable of waveguide or transmissin'line sections havfrequency shifts due to variations in load iming distributed reactance characteristics are pedance, F01- any 'terminal impedance 01 fan.. feasible. At lower frequencies, artificiai lines dom phase and magmtude -whieh 'wi11 provide a comprising lump Circuit Component-S mit!! be standing wave ratio of not more than 1.5' in a substituted for lines having distributed 'rcon- Wavegide system cennecting the load and theV stants. At any frequency. equivalentV cll'cuits stabilizer system, it is possible. in the absence of comprising combinations of suitable mutual ref modulating $1gne1s,t0 limit the frequency shift; flOtB-HCGS. lumped 01'v distributed l'eflctances and to one part. in fifteen thousand over the entire resistances, may be employed. range of'terminal impedances represented by It S Well knOWIl that the frequency Of a Senthese conditions. The improved operation proerator which includes two resonant circuits havvided by the instant system is due to the fact ine relatively Wldely dlflerent Qf' values Will' be that the theoretical limit of the resultat-it enescontrolled by the resonant circuit having Ithie tive HQ of the control impedanee may be shown higher "Q" value, and more ei'fectivelyI controlled to be 0111641911 of thesquared value if the higher Q clrcuit has the lower resonant 40 resistance. Itv also is well known that other parameters being equal, higher f'Q resonant 2 circuits, provide improved frequency stability in .of the Q of the control impedance. The limitsuch generators. ing 'factor is the loss in the impedance trans- The instant invention provides improved, subformation. The resultant high "Q" network r stantially linear freouenc'y modulationover that combined with great phase sensitivity with reattainable with prior systems, and although spect to modulating potentials provides high somewhat unorthodox in theory and application; sensitivity and fidelity of frequency modulation. Iit is readily adaptable to the frequency modula- Among the objects vof \the invention are to tion of signal generators at' any frequency. The provide improved methods of and means for frequency modulating network comprises a high modulating the output frequency of signal gen- "Q" Variable impedance of a complex naturen .erators Another object is to provideimproved which' is transformed to a new impedance with methods of and means for synthesizing control a higher Q and lower absolute value, and M resonant circuits for modulating thefrequency of -carrier wave generators. An additional: ob-

methods of and means for eifectively raising the g Q of a Variable resonant circuit.. the 'reactance of which is responsive to signal intelligence.

I Another object is to provide improved methods i of and means for frequency-modulating carrier signal generators by electromagnetic means. further object is to provide improved' methods 'of and means for frequency modulating carrier signal generators'by ionizable meansf- An additional object is tov provide improvedmethods -of and means -for frequency modulating carrier signal generators by electronic variable reactance means responsive to signal intelligence. A still further object of the invention is,to provide improved methods of: and means for providing a high "Q" resonant circuit wherein a high "Q" Variable impedance responsive to signal intelligence is transformed to a lower variable .impedance "value having a higher "Q". and then a predetermined value of said transformed varv as shown in Figure 1.

ters are changed even slightly it is possible for the new, simple equivalent circuit to contain a radically different potential and impedance.

The generator I, maybe considered as having load terminals t: and to' It would be advantageous to 'have terminals ti and t: available,

but terminals t: and ti are the only ones which vare accessible'. However, if Zme is of the form it will always be possible, by proper choice of an external circuit, to tune out the reactive term with an extemal series reactance :rm which is so that the oscillator may then be represented by the potential, e, in series withlthe resistance,-

' fint.

viable impedance is parallel-resonatedwith a reactance of opposite sign.

The prior. art and the instant invention, both as to theory and practical circuit configurations. will be described in greater detail by reference to 'the accompanying drawings of which Figures 1 to 13 are schematic circuit .diagrams illustrating the .mathematical discussion of the features of the invention; Figure 14 is a graph illustrating' said mathematical treatment of the invention; Figure 15 is a fragmentary perspective view of the coupling between the carrier signal generator and the frequency modulation network; Figure 16 is a side elevationai view of* a basic embodiment of the invention; Figure 17 is a cross-sectional end elevational view -of said basic embodiment of the invention taken along the section line XVII; Figure 18 is a fragmentary, partially schematic,

4 side elevational view of a flrst or electromagnetic cross-sectional view of a second or ionizable ernbodiment of the invention; Figure 20 is a fragmentary, partially schematic, side elevational, cross-sectional viewof a third or electronic embodiment of the invention; Figure 21 is a fragmentary, partially schematic, side elevational. cross-sectional view of a flrst modification of said third embodiment of the invention; Figure 22 is a fragmentary, partially schematic, side elevational, cross-sectional view of a second modification of said third embodiment of thelinvention; Figures '23, 24 and 25 are graphs illustrating the Operating characteristics of said third embodiment of the invention and said modiflcations thereof; and Figure 26 is a fragmentary perspective view of a modiflcation of said basic embodiment of the invention illustrated more completely in Figs. 16 and 17. Similar reference characters are applied to similar elements throughout the drawing.

Any oscillator or generator used as a source of energy has certain characteristics which for convenience may be expressed in terms of impedance concepts.4 The resulting equivalent circuits lmay contain many elements which may or may not be linear with certain parameters such as frequency.

In Figure -2 the'oscillator is shown as connected to any external terminal impedance composed of m branches each of which contains mn branches. If all of the elements in the extemal circuit of Figure 2 are pure reactances, with no real terms and if .rm-w, then the actual external -be allowed to radiate or to supply power to a. load.

To be useful. at least one of the impedances of the external circuit must be complex and therefore contain .a real term. By introducing only one real term in the external circuit of Figure 2 the actual circuit configuration becomes important since the rate of phase change, with frequency, at terminals ta-t4 will depend upon the particular configuration.

If Zon, is controllable, then it must' be so chosen that a large rate of phase change with frequency at ta-ti will also produce a large rate of phase change vat tr-ta- If there is no control of :tina then the extemal circuit must produce a large rate of vphase change with frequency at ti-tz andnot necessarily at ts-ti. i:

One other practical restriction must be imposed on the external circuits. At very Vhigh frequencies it is dimcult to measure impedances andv radical changes in circuit operation which will However, under any 'oneset of Operating condition's, this complicated equivalent circuit may albe easily detectable in monitoring equipment used during adjustment should occur near optimum adjustment of critical circuit values, so that proper initial adjustment may be made.

Obviously, an innite 'number of circuit configurations is possible.- To insure a correct approachto the' problem without becoming quite hopelessly involved in too many possible circuit forms, it is desirable to make certain reasonable aproximations which transform the problem to a much simpler one. The validityiof these ini- 'tial approximationsl may be examined when a tentative frequency modulation network has been4 found.

The basic circuit of the instant invention is shown in Figure 4. The impedance Z1 will-be -the parallel impedance of the two branches in i in simplifled form the plane A-A. The lines are of length L: and

le and may be either wave'guides, transmission lines. artificial lines, or equivalent circuits coni taininz mutual reactances andimpedances.

Referring to Figure 4, it is convenient to let the characteristic impedanoes" of lines L and Li be alike and represented Vhy Ze, and kthe propaaa-l i tion constant by P=a+ifi.

i Actually, of course. the lines will have some attenuation so that transmission equations. will in general have exponential attenuating factors, v

zratly, it may be assumed'that the distributed lr series resistance of the 'line per unit length ap- 'proaches zero and the distributed shunt resistance of the line per unit length approaches inflnity. Thus the hyperbolic functions may be replaced by their corresponding trigonometriezo functions. Acoordingly, the impedance Zl in the plane A-A is sin fiL cos BL|+ sin L;

Rationalizing, an exceedingly cumbersome expression for Z1 is obtained, which maybe written Zx=P+P' (4) in which p and p' are each functions of R, x, Rs, its, Zk, BL, and fiLn. i

-The various circuit constants must be selected and related so that the maximum rate of phase change with frequency in Zi at A-V-A is obtained. This may be accomplished by making venient to write i V where .3 3 65 t 1,'R- 41, axnd L R is practically independent of frequency for small frequency changes Af near f, but it is apxparent that the solution of the simultaneous Equations 5 to isimpractical. However, consideration of the desired result in view of the circuit of Fig. 4 'permits certain assumptions to be made which simplify the solution.

In Figure/i let L=0, and let R be the load resistance directly (or some transformedload resistance). By connecting in series with R a 17,5'

in i 'la-0% RUR 5 i reaetanoezwhleh-isafimotionoffrequeney,

i one element of lpersllel (referred, to a plans through A-.-A) resonant oircuit is provided. The

other element is R|+iea For maximum rate of 5 phase chansa with frequency at A-A. impedance R+i-i and 1h+iz should have the highest' possible Q values, By'using a shorted section of i low attenuation line itisseen that i (ll) ze=w| The branch Z contains the load resistance R. which limits the upper valuefor :c since, if z, is too large. the resonant resistance at A-A will be too high. The attendant difllculties' for a high resonant resistance have, already been discussed.l The result is that the Q ofthe branch R+iz will be limited quite severely.

i If, a line length Liisselected which will transform the impedance Z=R+Lr to Zz=Rz+ic in which x and o S12) i i Ri+afl R+cF The absolute value of impedance l|Z| can be.

|Zt| and at the same time the ratio f If-I I R is transformed to a larger ratio R' This require is very important.

At the plane A-A, looking to the left,I the im- 40 pedanoe Zz is which reduces to' a more convenient form sei-(arsa I I Instead Of the inequalitles of (12), lt is con- I'rhus t is the Q min vof the transformed impedance to the untransformed impedance.

RLi-:t2 '(165 where U l. The product Ut may be maximized i Where the line length fiL will become the Variable.

'considering frequency changes of the form f=f 1+o i transformed to a smaller numerical absolute value attans where fo is the initial frequency, I man be Using Equstions 19 ena 20 in is, it is seen that om i i U--RA/Q'LF1 and if Q 1 IQ| 1 R Q z conditions are. not opposing.

From Equations 2 1 and R Ut-R-t n From Equations and 14 tee-eleml i (27) Ilfhe roots are se 2 -1 cos 2L=0 L=2i 'jf- (28) where n is any Integer, and

. 22: tan 2L= zil-(-( (2 ZI. Zl,

If a. matched load condition is assumed for the terminal impedance R=Z,c but :N60 Equation 29 reduces to tan 2fiL=v-2-a?I ena to fuiflu Equetien 17 ten zL-o and eL=(2";1) f (ao) n is any Integer.y

-use oi Equation 14 and these quantities may be compared with R and a: respectively. In each case assuine *I z "z,,} (35) i Then for the flrst condition, Equation Bi zzlf;8 Zt=Rt+2$t= 'IfZk (36) 2Z Rg= zTk and xt: Zk The initial impedance Z was zl=R+ie=z,,+iz so that the quantities U, t, Q=fl and Qrinay be compared :I |U|=;,-,-ZIG (37) iLi m Rtx-2Zle (38) Q==zk (se) 0:2 Q, 1%:=2 Zk-2 (40) The interesting' result is that 'i'hc conditions to be investigated occur, thcreim. lt I .m'eeen case-*m enas, mey be obtained by the and at the same time It has been assuined that Q 1, so if Z=R+iz is parallel resonated with a resistance :c'-a

Ithe resonant resistance is I 0 Rm=fn=Q (42) while it i z.=%'i -izk' is parallel reson'ated 'with a reactance :ct'eL-zt, the resonant resistance is at the same time the parallel resonant resistance For the second condition of Equation 82 'rne initial z=n+fz m parauei with '-m res onant resistance is apparently the only difference is thatthereactance :rt changes sign.

For the third condition of Equation 33 Z|=Rs+$c=zk+ I (52) and in similar fashion stR t=lf=1 (54) o==z (55)' R,2+e,fl=\/Rf+e2 (57) For this condition nothing has been changed or iof Therefore it may be concluded thatthe flrst two conditions are identical except for change ofL sign of the reactance :stand both are very useful.

Condition three is of no value and condition four must be compared -with the first two..

The physical circuit conflguration which will provide th'e arrangement of Figure 4 to the left of the plane A-A must be determined. 'This may be done with sections of. transmission lines or with sections of waveguides having the nec- 'essary modiflcations; The circuit of Figure 5 I will provide the arrangeme'nt of Figure. 4 to the left of A-1A. The circuit is composed of R, the

shorted length of line Le' and th'e line L. How- 4 ever, if the reactance .'c, where z=Zr tan pl'a, is

large as compared to R, as is necessary, it will be diflicuit to deliverv suflicient power to the resistance R. Therefore, it is convenient to substitute the circuit of Figure 6. The line Ls initlaily is selected to be approximately-'mr wavelengths longand the waveiength. is varied from A to a(1+a) wh'ere it is'assumed that o '1. Thus lL,s=nf+a (67) and phi changes' in the following manner f i Li-=(M+.4 )(1+6) M (6.8)

The resistance'Rs, where Its-P0, is inserted to provide a-decoupled resonator. -The equivalent circuit, using sections of wave guides, is shown in Figure 7.

-Accordingly, a rapid rate' of .reactance Vchange i -in a: with frequency is obtained. This condition The initial z=a+is m resonant resistance is V I 1 .R},.===Q i (65) I while the transformed paraliel resonant resistalldelsV R....=z,.=%' i (66) parallel with ,-1L'c)- will be as satisfactory as if x Rand the dimculty in delivering power to R is avoided. In

Figure 6'the effect of the discontinuity introduced by inserting Rs as shown must be determined. This may be done by referring to the auxiliary circuit of Figure 8. It may be shown that the resonator above Rs, but including Rs, in Figure 6 reduces to the circuit of Figure 9.

.In similar fashion the effect of the cut-off window between Ls and the' resonator Le in Figure 7 also must be determined. It is useful to introduce the auxiliary circuit of Figure 10 for this purpose. It may be shown that the resonator above the cut-off window, but including the window, in Figure 7 reduces to the circuit of Figure 11. I

.apparently it is not generally appreciated that the resonators of Figure 9 or Figure 11 when viewed-from Rs or the cut-off coupling window respectively, or at a plane nr removed may be made to operate either as series type or parallel type resonators;

In the wave guide case this'is eifected by choice of window size as compared to that window size whichmatches the resonator to 'the wave guide. This fact isespeciallywimportant. For simplicity it may be assumed that the lines to the right of ax, in Figure 9 and to the right of window :vw in Figure l 1 have no attenuation. Then for series type voperation as viewed from Zm and Zita respectively, 9:-, and cut-off guide cLc, which is represented inl-Figure. 11 .by zuw. may be omitted for all practical purposes. At resonance in Figure 9 and Figure 11, m will always. be mr. In both cases the resonators will display all the charac-V teristics of series resonators, and at resonance the i which for Rs-O reduces to reactance of line La which is iZi: tan Lz, are 25 which reduces y 70 attans f ii I 12 acteristic high resonant resistance. This maybe and for pelle small done as follows: l I

In Figure 8, a line of characteristic impedance I (L,)'+1("+ ,.)('3FL) (76) Z: is shunted with a resistance Rs-m, and the ter-g I ZW=ZII 1 cLc z mination Z: is provided as shown. Then v 5 y T 2. I Rs (I +tan, 4,) +itan W [1 Rs For the special case where fie-L 1 zL ZhZn-I-Rs R Zri-Rs Z 51+ +l L (77) s .w= )e i 4 H (Zri-Rs) tan w M (69) so that it appears that the thin cut-off section of wave guide serves as a lumped reactance fx, which is V a'H'* R 1 ZL=Z|;' kB -2l=zg I i$w=i ;)cLc 1 w Ze'l' Again in Equation 67 the value of 4 is chosen so Disregarding the real part of Equation 70, lsince thai; lo in Figure 11 IS in the second or fourth that is a term which will aflect only'the Q, the quadrant. The reactance iw is resonated with discontinuity provided by Rs is equivalent to the the negative reaetance Zz tan La at the desired reactance iL in Figure 9, frequency. The resonant resistance is a function The reason for introducing 4 in Equation 67 01' is apparent. If o is large enough so that the inz' Z I. tan L2 and increases with increasing put reactance of La is negative, the arrangement of Figure 9 is obtained where in. and the negative parallel resonated. The line L: is never nr at :vw resonance but instead is always in the second or Ze tan Li fourth quadrants. The impedance Zai in Figure At any one frequency the magnitude of the par- 9 accordinly may be a large resistance at resallel resonance resistance is controlled by proper onance and .has all the characteristics of a parl choice of u, fieLe, and Lc. Again at resonance allel resonator when viewed mto the left of L. pL: efi mr.

The same situation exists when wave guides are Since, for some applications, it may be advanused with a thin cut-off window. In Figure 10 a tageous to operate the resonators of Figures' 9 thin section of cut-off guide is terminated in a yand 11 as series resonators, the condtiions for section of guide of characteristic impedance. Z: this operation must be determined. The right which is terminated in turn by Zr. In this case hand termination in each case becomes R- 0.\ the propagation constant of the section cut-off The impedance Zm must be determined. This guide is i p time the line is mr long initially at resonance,

2', -Tz and changes from mto mr (1-5-6) as the wavev=1-)/1-() (71) 40 length in the guide is changed. Again Rs 1, where Ao is the free space wavelength and a is the and width of the guide. As usuai, beyond cut-on m 1+a f 1+s (79) v 1 k I Then a- Rsl:cosl(n ---mr8)+si *(Lw so that Equation 71 becomes i Zk f 14.5 D 1+5 2* t 2 n R 2 T -e ica-1 'Y M (2G (72) Zm=iZIF+ zs1n 1+ cos mr 1+ zh l Thecharacteristic impedance of the section of 0052 M fl)+[afilsn n 1f 2 cut-off guide Zke must be a negative imaginary so 1+ Zk 1+ (80) that p Zu= -izb (73) And when Zai is connected to parallel with Rs, z'= I For the symmetrical case a=l, and n even, Equation 81 reduces to Then, the input impedance of the thin section of cut-on guide which is terminated in Z: is

1+tanh .L.) p. I As would be expected Z' has\.the characteristic form of impedance variation of a resonaton annans 13 If line L: is' considered to be the resonator and if the equivalent Q is expressed as then Equation 71 converts to the charaoteristic form i w i and the phase change of Z' with frequency is proportional to Qias would be expected.

Similarly, for Figure 11, BL: will be mr 'at resonance and change-to mr (1+6) with changes in wavelength in the guide. The termination for Since the impedance change near resonance is to be used 'for frequency control purposes, it is desirable to operate the cavity resonator near cut off. Accordingly the change in wavelength in a rectangular guide (also used as a resonator in this application because of convenience) lg, either with frequency or its inverse, to, the free space Z* 1 Jos (man) I wavelength is important.

The guide has cross section ab and a b. The wavelength in the guide is i du, v IHF-* ToT/-i [1-(a) For standard X-band guide 2a=1.80 inches and at 9310 megacycles per second \o=1.27 inches',

which indicates that the rate of change of* wavelength in the guide is 2.82 times the rate of change of frequency. The factor 2.82 would, of course.

' be greater by Operating nearer cut-o considering the circuit of Figure 7 with the T (se) q Junction shown in Figure 12, under conditions where lo is the free space wavelength, b a. and the special case where c=b.

14 i i Yi is the normalized adrnlttance extrapolated to Z=0 for the left leg. Z 0'. Ya is the normalized admittance extrapolated to Z=0 for the right leg. Z 0. i i

Ya is the normalized adinittance extrapolated to=b for the vertical leg; u b. U i

Y1=Y==l for a travelling wave propagated in the +Z direction.

the wavelength of the longest TE wave propap gated in the guide; For thiscase assume b=c. Thenva1=.'368, az=10.4, and aa=2.49 for a standard z-band wave guide. i i i Considering the case where wave propagation is from the left. where the vertical branch has an admittance Ye, and where 'the right'hand' branch has a matched termination and quation becomes i [1+1o.4(-.36s+i2.49Y,)1Y,-

Y 2(i.368+2.49Y,) 1 1+10.4(-.368+i2.49Y,-2Y1) v or U i Y -2.82+4.98Y2+i(25.9 Y2+.735) .98)

1 -2.s2+i(25.9,+2o.s) i

It is sometimes easier to use a rationalized fc of Equation 98.\ If Y: is of the form Y,=y(cos 0+ sin 0) (99) V 23.25+249.8y sin 04-5441] cos 0+671y2+ (56.52+505y sin 0-\-103.8y cos 0-129 gi) 438.94-1461/ sin 0+1080y cos 0+671y2 In Figure 7 the resonant resistance of the resonator may be expressed in terms of the characteristic impedance of the line La and may be considered as a termination' for La. The impedance of the resonator ofl resonance as a termination for L; should be considered to determine the rate of change of phase angle and re- -actance with frequency. It is convenient to 'consider the resonant resistance' and impedance values VgQ above and below the resonant frequency. The resonant resistance is auZr where Z:

is the characteristic impedance of Ls and aoZris i' either greater than, or less than Zr, as has been shown. The impedance at a frequency 1/2Q higher than the resonant frequency will he q and the impedance at a frequency tQ lower than the resonant frequency will ,be

Z i fis-*W To complete the frequency control circuit of Figure-i, it is only necessary to consider various terminations for L: in Figure 7 which involve travelling wave propagated attans.

various values of ao..and the. transforming action of La. This terminating admittance is the Y: of. Equation 98. The admittance Yi isy then the termination for line L in Figure 4. Line L transforms Yi to a new admittance at the plane A-A. The corresponding impedance at A-A is then parallel resonated with the reactance provided by line Li.

This final resonator is then connected directly to the oscillator. or to the oscillator through a ooupling line or circuit.

It is necessary flrst to determine the line length L; in Figure 7 which will give maximum rate of phase change at the :lunction with line L, all for a change in phase at the resonator. which is then the termination for Ls. The resonator termination in terms of Z: is aoZr. At resonance ac is a real positive number, and ofl resonance it .is complex with a positive real part, so that ao=ai+iai (101) Accordingly, the normalized input impedanceof line Lo as viewed from line L is p 1-202 tan Li+(ai? 012) tan BL: (m2) and the phase angle is measured by will-tan* flLi)+(l-ai'-ai2) tan fiL 1.04 ai 1+tair L.) p a (m3) i Ze in Equation 102 is the Y: of Equation 98.

Rewriting Equation 103 P= k ai (cos2 BL: sin2 fiLa) (1 ai' af) sin Li cos fiLi 'I'he region where az is zero initially and then assumes small positive and negative values is of primary interest. Equations 100 and 107 give Obviously, from Equations 108, 102 and 98, li' Yi in Equation 98 is to undergo maximum rate of phase change with small changes in az, from zero, there are two choices for fiLe.

1. If the resonator termination on Lo (Figure 7) operates as-a parallel resonant circuit ao 1 and Lo s m- L;=0,I-, 271- mr (109) 2. If the resonator termination on (Figure 7) operates as a series resonant circuit ao 1 and 1a=nir initially, then from Equation 108 =l-f[-2ag cos 2614-8111 2314]:0

, 2 I pia-g; (110) Condition 1 is preferred since -the high ratio. and necessarily low attenuation 5 i line transformer which is automatically incorporated in condition 2 is avoided. However, if extreme care is taken to make the -line'transformer very low loss, condition 2 .is also capable of providing good results. Since condition- 1 is the preferred condition, it may be assumed in Figure. 7, fiLi (at resonancehnr, La=m-. but it should be understood that the alternative condition L, (at resonance) 111,;8La 2112:11:

may be substituted,.although the results then are likely to be poorer mainly because of the dif flculty in making the The better condition may be determined. For various resonator terminations aoZk for line Le,' Where a0 1, fiL2=n7n Equations 98 or 99 provide the values of Yi for the various indicated conditions of table I. Conditions at resonance and off resonance by:1/Q in frequency are shown.v

Table I [Resonator terminations aaZi for line L; in Figure 7.]

and where n- -L As indicated heretofore, larger values of n merely increase the phase sensitivity, as is desirable, especiallylf thev wave guide is operating fairly for line L are i *ff taken from Table I. Then, for 2n-1 L-( 4 the transformed value of Z is Ztwhich is As shown in Figure 13, Ze is to be parallel resonated with -zs l(112) and When Ye and Ya are connected in parallelthe resultant admittance is At any other frequency :1:1 and Rt become :r and r, respectively, and the parallel impedance becomes eL-'flllf sis-mf Y. (normerna-lo mini-:0115051100 Ya Ze Z] .02 .1175- 1773- .700 /-81 20' 5.00 25 .02 (1+i) .1204- 1751- .700 /-80 14' (4.40 105021I .02 (i-i) .1050-1822 .830 /-82 42' (5. 22+i2. 77)zr .04 .145 1. 775- .700 /-79 25' 3.2szl. .04 (1+i) .1755- 1729- .750 /-76 27' (3.13 1. 582021. .04 (1-0 .1335- i.sa8= .850 /-80 57' (4. 04+i1. 8102;l .10 .251 1.820- .850 /-730' 2.035 z. .10 (1+i) .201 1.003- .720 /-7226' (1. 200- 103202.. .10 (1-1') .247 -11.0 =1.03 /-'I608' (2. s15+12.02)z1 .20 .377 -1.705 .875 /-6350' 1.02 z. .20 (1+1) .380 -1558 .050 /-55 47' (1103- 1.442)z,. .20 (1-1) .520 1104 =1. 162 /-6326' (1.s05+ 180102. 1.0 .900 -L 570 =1.1s /-80 56' w1.31 2,, 1.0 (1+i) .304 1143 .410 /-19 51' (Ass-1001M21. 1.0 (1-1) 1. 270 -1. 270 =1.300 /-12 20' (1.17+1.450)z,. 5.0 1.105 -1.15a -1202 l-7 18' .00 z f 5.0 (1+i) 1. 125 -L000a=1. 120 /-3 31' (.030-1.0052)z1 5.0(1-1) 1.42 1050 =1.42 /-2 15' (.010+i.1505)z.

Comparing the initial phase angle of the resonator, Yz, and the phase angle of the control im- -Table III. i Insertion' loss as' shown in the graph of Figure 14.

near cut-om The terminations Cpedance Zi, it is evident'that theresohanee characteristic of Zl is not symmetricai about the resonant frequency, but becomes approximately so in the region Y2=0.2 to'10.1. i Also, the phase angle changer of the loaded resonator Zi in the same i lregion Y2=0.2 to

J 0.1is equal to, gor' greaterv than, the original change in phase angle of Yi. L

It is possible to' improve the symmetry about resonance by operating with filoa=13 30" for which Yi=1, but only at the expense of reduced rate of change of phase angle ofZi. Use of an irls i to provide. a Iump'ed' reactance in llo to provide the equivalent of Operating fiLa atlength La=n1r+i3 30', is possible.

The entire control network may be considered as e, working. into a matched terminatloli Ro eRo 1v e2 J i P Ro+R0) R0=4=R0 (119) which may be employed as a reference condition. The power delivered to a matchen -termination when the stabilizer is inserted may be compu-ted readily. The difference -in the power is the insertion loss. The power delivered to a matched terminatlon for various values of Yz is shown in a function of Yi is Table III v [Resonator terminations aoZy. for line L; in Figure 7.1

Y; (normalizedhq Y Power in Matched Insertion Termination Loss Per cent 02 064302 74. 2 04 07800l 68. 4 10 ll22el 55. 0 20 15561 38. 0 1. 0. 23162 7. 6 5. 0 .248eI 0. 9

Reference power with no stabilizer is .2505.

'erating parameters'is feasible. For ao= 10 the insertion loss is 55% The average loaded Q for the synthetic resonator Zl. for a0=5, is about one times the -unloaded Q of .the initial resonator and the resonance characteristic again is not quite' symmetrical about the resonance frequency. A-t' s =5 the insertion loss is 38% i The performance does not change rapidly for values of ao between about three and ten. For a value of a0=3, the insertion loss is about 23%.

The final choice of ao is a compromise; 'OperationV is somewhat better for ao==5 to ao=10, but' not tremendously better than for a0=3. Therefore,

point on its characteristic,

power output for the os'cillator, i

19 any value of ao between about 3 and 10 is satisfactory.

The case where should be considered. lFor the same various values of aa, take as terminations for line L values of L i r Y! from Table I. For simplicity, consider the case As before, corresponding values of Zl, the mean value of the control impedance may be computed from Equation 118. The results are shown in Table IV. Comparison of phase angles for Yz at resonance and at frequencies l/2Q above and -below resonance, with the corresponding phase angles of Zi, indicates that the rate of phase Vangle change with frequency is much slower for Z1 than for Yz. Also conditions are much worse than those in Table II where 21t- 1 L Was TT Table IV [Resonator terminations auZr for line L; in Figure 7.] i L-zn-Tlf Li=1|f Y, (normalimm- Y: (normalized) Zl (normalized) Zl .0743+i.1240 .270Zr 02 (1+{) .0847+1. 1365 257 l. 1475)Z 02 (l-) 0640+1. 0958 .206 +l. 111) Z 04 0955-14. 1085 222Zz 04 (1+i 1170+i.' 148 278 i. 181) Vt 04 (l-i 0792+1. 0848 l655+1. 0818) 71 10 1520-14. 0809 195Zt .10 (1+i) .15oo+i. 165 (.320 -i.116)z1. v. 10 (l-) 1214-14. 0127 1175-l-i. 389) Zz 20 239 -l-i. 0793 272ZI. .20 (1+1') .298 +i. 214 (.439 -1.122)Z1. 20 (l-i) 232 i. 0735 184 +i. 00625) Z; 1.0 .564 -1.0803 57621: 1.0 (1+i) .sas +i.se 438 +;.o316)z. 1.0 (l-) .785 i. 2155 828 +1. 0619) Z: 5.0 868 i. 164 895Zr 5.0 (l-H) 937 1098 874+i. 0245)Zr 5.0 (1-i) .909 l.323 1.14 +1.088)Z1.

Equations (33) which lead to the results of Equations 56 and 57 indicate that a line L=n1r will not give good results. This prediction may be checked by numerical calculations. For L=(2n-1)1r and the special case where n=1.

Z Yi (121) which is the normalized value of' Zz. The results are shown in Table V. As, predicted by the general analysis, the rate of phase angle change of Z1 with frequency departures above and below 20 sensitivity of a longer line. Also, it is advisable to have the wave guide operate fairly near cut off so that the ratc of change of wavelength in the guide is greater than the rate of change of frequency or of free space wavelength.

Table V [Resonator termination MZ for line Li in Figure 7.] pL=mf Li=nf Y. (normniwn- Yz'(normalized) Z; (normalized) Zl 02' 3. 55 15. 93 13.4 02 (l-H) 3. 29 1.531 (11.7 13. 67) 71. 02 (1 i 4. 83 17. 23 (13. 05-1-19. 32) 7: .04 4. 57 1520 10. Zl: 04 l-H) 3. 29 14. 17 7. 70 14. 98) 7:. 04 1-i) 5. 89 16. 31 (11. 65+i5. 69) Z). 10 i 5.24 12. 79 6. 707,1: 10 (1+i) 3. 03 13. 33 (4.91 i1. 875) 7; 10 (1-1') 8. 14 1.853 (5. 38 +1. 586) 7,1 20 3. 77 il. 253 4.19Zh 20 (l-H) 2. 23 11. 60 (2. 83 i. 823) 7,1: .20 (1.-i) 3. 92 +i1.24 (3. 00 l. 086) 7), l. 0 1. 735-1- i. 247 1. 835 7.1, 1. 0 l-i-i) 883- 1.928 760+ i. 0988) 7-1. 1. 0 1-1') 1.186-I- i. 325 (1. 245- 1. 1315) 7.: 5. 0 1. 112+ i. 210 l. 7-1; 5.0 (l-l-i) 1. 055-1- i. 123 (1. 070+ 0427) '71k 5.0 (1-) 976+ i. 3475 (1. 03l+ 1.0555) 71k Couplng of modulator to oscillator Any of the usual types of coupling to the oscillator may be used. In the case where the oscillator is a magnetron a particularly useful type of coupling is shown in Figure 15. A coupling loop, not shown, is placed in and tightly coupled to the magnetron cavity or cavities and connected to a concentric line. The outer conductor 5 of the concentric line is terminated in the lower wall 'I of the Wave guide as shown. The inner conductor 9 extends up in to the guide a length La. As before, the width of the guide is a and the height is b. The coupling loop in the magnetron cavity, length of concentric line and antenna of length La will, in general, present an impedance which can be represented by a lcomplex number of the form By proper choice of distance h of the reactive stub lll, the reactance :cm may be tuned out so that Zmt becomes Zim=Rin (123) The greatest change in Operating frequency of the magnetron cavity results whe the current in the coupled concentric line 59 lgoes through its maximum value. This condition should occur if the radiation resistance of the antenna La goes through zero. This condition results, in turn, if the guide impedance vin the plane A-A goes through zero.

If the antenna radiation resistance does become zero, or approximately zero, the power output of the magnetron will be very adversely affected. Therefore the radiation resistance chosen must be a compromise between a very low value which would give remarkable modulation control, and a somewhat higher value which will vstill provide acceptable control.

Inspection of Table II. especially in the recommended region ao=3 to 5, indicates that this second condition may be met. The problem may be considered from either the point of view of the antenna La and the effect thereon of the 'impedance Zi coupled to it by the guide, or from the point of view of the impedance Zi and the effect thereon of the antenna .coupled to it. In

'Also a:-:2b, thus the end area A1 is either case,A by proper choice of h in Figure thereactancemt must be cancelledout so that only Rim remains. Also, in either case the collpling factor ke of the antenna L. to the guide will i appear as follows: x

l La 2 'vrd lt.,\-2( b) sin2 where a, b,'and d are indicat'ed: in Figure 15. v If standard X-band wave guide, L=x/4 at the n i lo Operating frequency 9210 megacycles persecond,

and d/a=1/2, are employed, then k,,=2(.795)z sin21r/2=l.265- i (125) In the first instance; the antenna of resistance Rim has connected to it the external impedance Zi, but the coupling factor ka enters 'to make the equivalent external impedance kaZ1=1.265Z1.' In i a 22 and K;

where in is the free space wavelength. If the E vector is initially in a plane parallel to the crosssectional, or my, plane only one Wave of the form will be propagated. 'The initial electric vector intensity is A, and y is the propagation constant. No other modes will be propagated. If other modes were propagated the same analysis would hold providedw the integrations are changed to accommodate the new E and H distributions. For 3 cm. Waves, the standard. 1 x 1)/2" Wave .79 Rs. i h (126) lguide fulfills the conditions a i b o The length of resonator for Z=7l/2 is L-QA/22b.

Ai=-2 (128) and the area of the sides. carrying current is i A2=2aL2a2 (129) Assurning a uniform Substance for the walls, it follows that the respective end and side resistancesare i i n men Ez 2R0 'considering the ends first, the current distribution in the y direction is sinusoidal, and the average current along y is Imax a unit area of the sides The average current in in the Zy plane will be IaNZu) It follows; therefore, that the energy lossesin annans the ende and sides, from Equations 130, 131, 132, and 133 are as follows:

The energy loss in the ends is s p Ji=$I:...R., (134) and the energy loss in the sides is J,=1,-1:..; 2Ro (135) so that the ratio of the energy loss in the ends to that in the sides is i 15 If the Q of a resonator is defined as 0 Energy stored in resonator Energy loss'n resonator then the Q of a standard half wave resonator is i p i where Ja is the energy stored, and J; is the energy loss, in the resonator. i i i For L= ./2, .n win be J1+J2 so that from Equation 137 i i v i i i i p J n Q( ./2)=l-l (138) or so ao Fo are nator o o H n 2 long the Q becomes n-in-fa" .i n o i 'n 21,3'

where the primes place the energy on a per M2 section basis. Then i i Ja Q X =-(2n-1) (140) o 21LJ1 o For the limiting case n- Q =-3 141 ,x o

For the shortest resonator n=1, and

o QA/2=2 j; so Ithat the improvement in going from n=*-1 to n=w is i n & Qui-2 I o (142) The analysis heretofore has assumed a uniform wall material. Since the endls involve a soldering orw welding operation, it probably is more accurate to assume the end wall resistance is about equal to the side wall resistance. Thus,

00 the end wall energy loss is Js where J5= TR0 (143) and the side wall energy loss is 16 i U v J=p1mRo (144) The ratio of energy loss in end walls to energy loss in side walls is :means M "M where .11 is the energy stored in the length' M2. For i v where the primes again denote a per M2 section basis.

For the limiting case ng 2.! Qiwi=j1 (148) so that the improvement in Q in going from Equations 142 and 149show that the Q of a resonator does not increase iinearly with they number of half wavelengths of length for an asnegligible. The same equations, however, indicate that if the ratio of end wall losses tov side wall losses is high or higher than that assumed, it may be desirable to add half wave sections beyond this 3 to 4 value.

Thus it i; seen from the foregolng conslderations that variation of the reactive term in Equation 118 in response to signal intelligence, may, if properly transformed and coupled to the generator as explained heretofore, provide extremely efficient and substantially linear frequency modulation of the oscillator carrier frequency for reasonable frequency modulation swings as compared to the mean frequency, Various devices for accomplishng such' Variations of said reactive term, and hence effective reactance variation of the control resonator, will be explained in detail hereinafter. f

A first practical basic circuit configuration of the invention, adapted to waveguide construction, is illustrated in Figures 16 and 17.

An ultra-high frequency generator comprising a conventional magnetron ll', of which the magnetic structure is omitted for the sake of simplicity, is coupled to a transmission waveguide system |3 which is coupled to a load, not shown. The output coupling line |2 of the magnetron H includes a coupling loop, not shown, which is closely coupled to one or more of the magnetron resonant anode cavities. The end'of the magnetron output line l2, remote from the magnetron proper, is terminated in a short antenna 15 which extends into the waveguide transmission [3. Re-

'actance in the magnetron output line |2 is cancelled by means of a reactive stub I'I opening into tending' normally from and opening into the transmission line I! at a point on the tramsversel plane B-B intermediate the load and'the generator. The reactance of the control stub 2lis adjustable bymeans of a second tuning screw 23 projecting therein. The degree of coupling from the control stub 21v to the transmission line ll is determined by a coupling aperture device 25 in the control stub waveguide adlacent the point where it opens into the transmission'waveguide [3. The plane B-B of the control stub Il is selected to be some multiple of one-half wavelength plus orV minus 1/8 wavelength from the plane A A- of the magnetron antenna. Thus, by meansv of a thirdtuning screw 21 extending into lthe transmission waveguide l3 intermediate the planes B-B and A A, the effective transformation of the impedance of the control stub Zl provided by the impedancetransformer ll, (comprising the portion of the waveguide 'system |3 intermediate the planes A A and B-B) i may be adjusted at the plane A A which' is effectively the resistive termination of the magnetron antenna. V The reactive stub 2| and second tuning screw 23* may be considered to be a resonator only as seen from the coupling aperture 25. At the plane A-A of the magnetron antenna, the combinationof the stubv and tuning screw appear as an impedance. i

A fourth tuning 'screw 29 extending into. the transmission waveguide |3 on the opposite side 'I of the plane A -A from the plane B-B of the tem. The load is matched approximately to the waveguide transmission system l3 by means of a first conventional tuning screw 19 extending through the waveguide wall adjacent the load connection.

The frequency modulation network includes a closed waveguide reactive high Q stub 2| excontrol stub Zl provides means whereby some predetermined or mean value of the transformed impedance of the control stub may be resonated inthe plane A A at the output frequency of the generator ll. f

The characteristics of the control stub 2l and the second tuning screw 23 coupled thereto areH selected to have relatively high reactance withvas i high a Q value as conventional construction will permit. Thus, by means of the impedance transformation provided by the transformer M between the waveguide transverse planes B-B and A A, the resultant reactance at the plane A A due to the control stub 2| will be substan-v tially lower than'the reactance of the control stub itself, and will have a substantially higher Q value. The transformed reactance at the plane A-A thus may be resonated by means of 'the fourth tuning screw 29 effectively to provide an extremely high Q" resonator at the plane A A which will be effectively connected in shunt with the resonant cavity anode of the magnetron l I through the magnetron coupling line which includes the antenna l.

The Characteristics of waveguide T junctions of the type connecting 4the control im-pedance 2I'to the waveguide transformer I 4 are Well known and are discussed in detail in the literature. Similarly,the reactive effects of tuning stubsI coupled into waveguide transmission systems are well known, as is the specific structure of such reactive devices. Detailed construction and theoretical consideration of appropriate tuning Iscrews is included in the copending' application of Vernon D. Landon, SerialNo, 508,229, filed October 29, 1943, now Patent Number 2,427,107, issued September 9, 1947, which is assigned to the same assignee as the instant application. i

Since the carrier frequency generated bythe magnetron ll is controlled by the reactive characteristics of the control stub Zl, the magnetron may be efliciently and substantially linearly frequency-modulated by varying the reactance of 254 the control stub 2| in gence. For example, a conventional microphone response to signal intelli-I 33, responsive to sound waves, may actuate any known device (indicated by the block 35 identified as a reactance modulator) to vary the reactance of the control stub 2l. Various devices for this purpose are described hereinafter by reference to Figs. 18 to 25 of the drawings.

Adjustment and operation In operation, the magnetron ll is initially adjusted by any conventional frequency adjusting means included therewith to provide the desired output carrier frequency. The first tuning screw 19 is adjusted to provide adjustment of the load i coupling impedance tomatch approximately the 53, 55 which are closely disposed at one edge and load to the transmission waveguide I3 and to permit, in the absence of modulation signals, nearly symmetrical tuningon either side of resonance by means of the second tuning screwv23. The second tuning screw 23 in the control waveguide stub 2| is adjusted to tune the control impedance 2| to resonance, as viewed from the aperture 25, at the Operating frequency, and in the absence of modulation signals, as may be determined partially by initial calculations. The fourth tuning screw 29 then is adjusted to resonate the unmoduiated control impedance at the plane A-A of the magnetron antenna, Next, the third tuning screw 21 is adjusted to vary the unmoduiated impedance transformation at the plane A-A of the magnetron antenna to obtain the highest practicable Q value for'the control impedance in view of the resistive load thus placed upon the magnetron as explained in detail heretofore. The fourth tuning screw is again adjusted to resonate the unmoduiated control impedance more accurately to the oscillator output frequency. If necessary, the flrst tuning screw I9 is again adjusted to match approximately the load to the waveguide transmission system |3 under modulated or unmoduiated Operating conditions.

It is assumed that the reactive stub I'I adl'acent the magnetron antenna |5 has been precalculated or preset to provide the desired cancellationof reactance in the magnetron output line to the antenna |5. If necessary, an adjustable shorting plug may be included in the reactive stub l'| to provide adjustment of the reactance thereof. This feature is indicated by means of the'arrow and piston 3 I. p

Figure 18 shows an electrodynamic system for modulating the reactance of the control impedance 2| in response to signal intelligence. The microphone 33 is coupled through an amplifier 37 and an output transformer 39 to the voice coil 4! of. a conventional electrodynamic loudspeaker mechanism Whichincludes, for example, a permanent magnet field 43 having pole pieces 45 adjacent the voice coil4|. i

are more widely separated at the opposite edge.

Thus modulating signals derived from the ampiifier 31' provide an ionic discharge between the electrodes '53, 55. The discharge occurs flrst at the more closely separated portions of the electrodes, and as the modulating potentials increase, the discharge extends toward the more widely separated portions of the electrodes. Thus, variations in modulating potentials in response to signal intelligence eifectively vary the length and the reactance of the control impedance cavity resonator 2l, since the ionic discharge between the electrodes 53, 55 of the gaseous discharge tube 5! provides a conductive path substantially across one end of the cavity resonator element 21. and the position of this conductive path is varied in response to said signal intelligence.

As in the modification of the invention described by reference to Figure 18, the second tuning screw 23 is adjusted to resonate the cavity resonator element 2| to the carrier frequency, in the absence of modu1ating signals. Th'us the modulating potentials eiectively vary the impedance of the control resonator 2| in response to applied signal intelligence.

Figure 20 illustrates a third embodiment of the invention wherein the control impedance cavity resonator 2| is modulated in response to signal intelligence by means of a conventional elec- The voice coil support 47 comprises'a cylindrical member which is connected to a tuning piston 49 disposed within, and adjacent to, one end of the control impedance cavity 21. Thus, the piston 49 is provided with a reciprocating motion in the control impedance cavity 2i in response to signal intelligence derived from the microphone 33.

In the absence of applied modulating signals,4

the second tuning screw 23 "is adjusted to resonate the control impedance cavity 2l to the oscillator carrier frequency as described heretofore. Thus, reciprocating motion of the piston 49 in response to modulating signals modulates the reactance of the control impedance cavity to frequency-modutronic device which utilizes the variation in dlelectric constant in a coaxial line which includes a magnetron reactance modulating device. Such reactance modulating devices are described and explained in an article in the Journal of Applied Physics, volume 12 (1941), :at pages 856 to 858.

The reactance modulating device includes a section of coaxial line having an inner conductor Gl and a concentrically'disposed outer conductor 63. The central portion of the inner conductor GI comprises the thermionic cathode 65 of a magnetron 'type thermionic tube. The cylindrical anode 61 of the magnetron 'tube is separated from, and capacitively coupled to, wthe'outer conductor 63 ofv the coaxial line through the glass envelope 69 of the magnetron tube. A tuning piston 'Il is insulated fromthe inner conductor 6| of the coaxial line by means of a central insulating insert 13. The tuning piston 'H may be moved longitudinally alongthe coaxial line intermediate the conductors Gl, 33 thereof'to tune the line to the'desired mean reactance. v

A strong magnetic field is generated in the space occupied by the magnetron tube elements by means of a winding 15 surrounding, and coaxial with that portion of the coaxial line. The magnetic winding 15 is energized, for example, by means of a battery 1'1 connected in series with' Vthe output of a speech amplifier 31 Vwhich is responsive to signals from the microphone 33.

of the magnetron tube is derived from the secondary winding 19 of a conventional filament transformer 8l, the primary winding 83 of which is connected to a source of alternating potential, not sh'own. Asource of high voltag'e, not shown, is connected between the cathode and anode electrodes of the magnetron to operate the cathode at Ithe required negative potential.

Thus a rotating space charge is maintained in that portion of the coaxial line SI, 63 which is occupied by the magnetron tube. The effect of the rctating space charge is to vary the effective dielectric4 constant in thecoaxial line in the region occupied by the magnetron. Thus, since the dielectric' constant may be varied from negative through zero to positive values by proper selection of the strength of the magnetic field and the applied voltage between the magnetron electrodes, the effective reactance of the coaxial line may be varied between relatively wide limits.

The coaxial line is coupled to the control impedance cavity resonator 2| by means of a short coupling line 85 having coupling loops 81 and 89 disposed within the coaxial line and control impedance cavity resonator, respectively.

The graph of Figure 24 illustrates th'e variation in tuning of the coaxial line device as a function of the strength of the magnetic field of the magnetron tube. Since the magnetic field strength is varied in response to 'modulating signals derived from the microphone amplifier 31, it is apparent that the reactance Variations in the magnetron-modulated coaxial line will be refiected in the control cavity resonator Zl and will vary the effective reactance thereof as a functionof.

said modulating signals.

Figure 21 illustrates a first modification of the third embodiment of the invention, previously described by reference to Figure 20, wherein the magnetic field produced by the winding 15 of the magnetron tube is maintained at a substantially constant value by means of the energizing battery 11 which is directlyconnected to the winding 15. In this modification of the invention, modulatingsignals derived from the microphone 33 and amplifier 31 are combined with and effectively vary y the high potential applied between the magnetron cathode 65. and anode 61. For a predetermined magnetic field strength in the magnetron reactance modulating device, the effect of variation of th'e high potential applied between the cathode and anode electrodes of the magnetron is illustrated in the graph of Figure 23, Thus, by proper selection of the applied magnetron anode voltage, the effective reactance Variations in the coaxial line device, and hence in the control impedance cavity resonator 2I coupled thereto, may be efiiciently controlled in response to applied signal intelligence.

The graph of Figure 25 sh'ows the' effective change in tuning of the coaxial line reactance device in response to adjustment of the position of the tuning piston 'II disposed within the coaxial line device.

Figure 22 illustrates a second modification of the third embodiment of the invention, previously described by reference to Figure 20, wherein the reactance-modulating coaxial line and'the control impedance cavity resonator are combined in one unit to provide a coaxial line control impedance element 2l' which is directly coupled through, a coupling loop 9! to the transformer section I 4 of the waveguide transmission line I 3. As in the device described by the reference to Figure 20, the reactance modulation is accomplished by variation of magnetic field 28 strength' in the magnetron tube in response to signal intelligence. that the coaxial line control impedance 2l' may bev coupled in any other known manner to the waveguide transmission system l3. It also should be understood that the efiective dielectric constant of the portion of the coaxial line control impedance 2| in the region occupied by the magnetron reactance tube may be varied by modulation of the anode potential thereof, as illustrated and described by reference to Figure 21.

In Figure 26, a modification of the basic circuit conflguration, shown in Figs. 16 and 17, includes a cylindrical very high Q Variable control reactance 2l" which includes a tuning piston 3'I, the longitudinal yposition of which may be adjusted by means of a micrometer screw 39. The control reactor 2l" is coupled to a T junction H' which extends from the narrow side of the waveguide transmission system l3. A second T junction 43 extending from the opposite narrow side of the waveguide system |3 includes the third tuning screw 2] which is employed to vary the coupling of the control impedance 2I" to the impedance transformer M. The first tuning screw l9 is operable through the transmission waveguide wall intermediate the plane B-'B of the control impedance and a load. not shown. The magnetron generator has been omitted for the sake of simplicity. The reactance modulator 35 for the Variable control reactor 2I" is shown in block form, and may comprise any of the devices described heretofore by reference to Figs. 18 to 25.

The higher Q control impedance results usually in higher values of resonant resistance and Vhigher reactances at the coupling aperture 25 opening into said control impedance at frequencies slightly off resonance. This Would result in anunfavorable situation if used in the arrangement of Fig. 16 and Fig. 17 in which transmission and control waveguide branches l3 and M are substantially in series insofar as the impedance transformer M is concerned. since under these conditions the power delivered to the load would be small. i

For this reason vthe T junctions of, the type shown in Fig. 26, in which the transmission and control waveguide branches |3 and 4I' (with the additional reactance of the tuning waveguide stub 43) are substantially in parallel, is used with a high, Q control impedance 2l", since the high impedances are then in parallel with the useful load.

-Since the impedance transformation and resonating is, otherwise similar vto that described' in -Figures 16 and 17, the effective control im- Thus the invention disclosed and explained d herein comprises several embodiments and modifications'of a frequency modulator for carrier wave generators wherein a Variable impedance It shouldV be understood x Variable control impedance is varied in response to signal intelligence to modulate efllciently the carrier frequency of the generator." Circuits" havingrapidrates of change of phase angle with frequency are employedand. critical' optimum line lengths are determined to provide practical and eflicient circuit configurations. Several devices are disclosed for Varying the reactance of the Variable control impedance eitheri electromagnetically, ionlcally or electronically in response to signal intelligence. i

It should beiunderstood that several sections of the control impedance and impedance transformation elements of the circuit configurations described may be .cascaded to provide aw more eflicient modulation system. However, circuit adjustment in such a cascaded waveguide systemv may become quite difficult, due to present waveguide measurement limitations and coupling technique.

I claim as my invention: i p

1. The methodvof employing a Variable control impedance for modulating the frequency of a signal generator comprising'the steps of transforming the impedance Value of said Variable impedance to a lower Variable Vimpedance value having a relatively higher Q, resonating a predetermined Value of said transformed impedance Valuesubstantially to said generator frequency, andishunting said generator by said resonated transformed Variable impedance Value;

2. The method of employing a Variable control impedance for modulatingthe frequency of a signal generator comprising thesteps of transforming the impedance value of said Variable impedance to a lower Variable impedance Value having a relatively higher Q, resonating a predetermined value of said transformed impedance value substantially to said generator frequency, shunting said generator by said resonated transformedvariable impedance value, and cancelling normal coupling reactance between said generator and said resonated transformed impedance.

3. The method of utilizing a Variable control impedance for modulating the frequency of a signal generator coupled to a load comprising the steps of cancelling normal coupling reactance from said generator, transformingl the imped-l ance valuelof said Variable impedance to a lower Variable impedance Value having a relatively higher Q, resonating a predetermined Value of said transformed Variable impedance value substantially to said generator frequency, and shunting said reactance cancelled generator coupling by said resonated transformed Variable impedance Value.

4. The method of utilizing a Variable control impedance for modulating the frequency of 'a signal generator coupled to a load comprising the steps of cancelling normal coupling reactance from said generator, transforming the impedance value of said Variable impedance to a lower Variable impedance Value having a relatively higher Q, resonating a predetermined Value of said transformed Variable impedance value substantially to said generator frequency, shunting said reactance cancelled generator coupling wby said aving-V ahigher y 'i ananas s seieteaisi w resonated transformed impedance Value, and' coupling said load to said generator through said impedance transformation.

5. The method of utilizing a Variable control impedance for modulating the frequency of a signal generator coupled to a load comprising'the i steps' of cancelling normal coupling reactance from said generator. transforming the impedance i Value of said, Variable impedance'to a lower Variable impedance value having a relatively higher resonating a predetermined value of said transformed Variable impedance Value substantially to said generator frequency, shunting said reactance cancelled generator coupling by said resonatedV transformed Variable impedance value, coupling said load to said generator through said impedance transformation, and matching said load tosaid load coupiing.

, 6; Themethod of providing a reactance modulated high-Q resonant network including a Variable impedance element comprising the stepsV of transforming the impedance value of said element to a lower impedance value' having a relatively higher Q Value, resonating said transformed impedance Value and reactance modulating said Variable impedance element;

7. A high-Q resonant network including a high Q impedance element, means for reactance-modulating said element, means' fortransforming said modulated element to a lower impedance having a relatively higher Q Value, and reactive means connected to said transforming means for resonating said transformed reactance-modulatedireactive means for *resonating a predetermined Value of said transformed Variable impedance substantially to said generator frequency, and means for connecting said resonated transformed Variable impedance in shunt with said generator;

9. Apparatus for modulating the frequency of a carrier signal generator having a frequency determining resonant element, including a high Q control impedance element; means for varying the impedance of said element in response to signal intelligence, means for 'efrectively transforming said Variable impedance to a lower Variable impedance having a relatively higher Q value, reactive means for resonating a predetermined Value of said transformed Variable impedance substantially to said generator frequency, and

means for connecting said resonated transformed Variable impedance in shunt with said generator resonant element.

10. Apparatus formodulating the frequency of a carrier signal generator-.having'afrequency determining resonant element, including a' load coupled to said generator, a high Q control imwpedance element, means for Varying the impedance of said element in response to signal intelligence, means for effectively transforming said Variable impedance to a lower Variable impedance having a relatively higher Q Value, reactive means for resonating a predeterminedU value of said transformed Variable impedancesubstantially to said generator frequency, and means for connecting said resonated transformed Variable impedance' in shunt with said generator resonant element and said load. i

11: Apparatus for modulating the frequency of a carrier signal generator havingv a frequency determining resonant' element, including a load, a 

